Progressive addition power lens

ABSTRACT

A system and method for designing a progressive lens. Mean power is specified at points distributed over the entire surface of the lens and lens height is specified around the edge of the lens. Lens height is determined at the points consistent with the specified mean power and the lens edge height in part by solving a partial differential equation of the elliptic type subject to the lens edge height as a boundary condition. A successive over-relaxation technique may be employed to converge on the solution to the partial differential equation, and an over-relaxation factor may be determined to most efficiently relax the equation.

[0001] This application claims priority from international applicationnumber PCT/GBO2/02284 filed on May 31, 2002, the contents of which arehereby incorporated by reference in their entirety. This internationalapplication will be published under PCT Article 21(2) in English.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] The invention relates generally to progressive addition powerophthalmic lenses and, in particular, to an improved system and methodfor designing such lenses.

[0004] 2. Description of the Related Art

[0005] Bifocal spectacle lenses have been used for many years by peoplesuffering from presbyopia, a medical condition that causes loss ofaccommodation of the eye with advancing age resulting in difficultyfocusing. Bifocal lenses provided a solution by dividing the lenseshorizontally into two regions, each having a different optical power.The upper region of the lens was designed with the appropriate opticalpower for distance viewing, while the lower region was designed forcloser viewing (e.g. reading). This allows the wearer to focus atdifferent distances by merely changing their gaze position. However,wearers frequently experienced discomfort due to the abrupt transitionbetween the different lens regions. As a consequence, progressiveaddition lenses were developed to provide a smooth transition in opticalpower between the regions of the lens.

[0006] Conventionally, progressive addition lenses are usually describedas having three zones: an upper zone for far vision, a lower zone fornear vision, and an intermediate progression corridor that bridges thefirst two zones. FIG. 1 is a diagram of a typical progressive lens shownin vertical elevation (plan view). The lens has an distance zone 2 witha given, relatively lower mean power and a reading zone 4 withrelatively higher mean power. An intermediate progression corridor 6 ofvarying and usually increasing mean power connects the distance andreading zones. The outlying regions 8 adjoining the progression corridorand the lens boundary 10 (i.e. the edge of the lens) are also shown.

[0007] The goals in designing progressive lenses have been to provideboth essentially clear vision in upper and lower zones 2 and 4 andsmooth variation in optical power through the progression corridor 6,while at the same time to control the distribution of astigmatism andother optical aberrations.

[0008] Early design techniques required the lens to be sphericalthroughout the distance and reading zones, and employed variousinterpolative methods to determine the lens shape in the progressioncorridor and outlying regions. These techniques suffered from severaldisadvantages. Although the optical properties of the distance zone,reading zone, and progression corridor were usually satisfactory,regions adjoining the progression corridor and lens edge tended to havesignificant astigmatism. Interpolative methods designed to compressastigmatism into regions near the progression corridor yieldedrelatively steep gradients in mean power, astigmatism and prism. Theresulting visual field was not as smooth and continuous as would bedesirable for comfort, ease of focusing, and maximizing the effectiveusable area of the lens.

[0009]FIG. 2 shows a three dimensional representation of the mean powerdistribution over the surface of a typical progressive lens design. Meanpower M is graphed in the vertical direction and the disc of the lens inshown against x and y coordinates. The disc of the lens is viewed froman angle less than 90° above the plane of the lens. The orientation ofthe lens is opposite of that in FIG. 1, the distance area with low meanpower 12 shown in the foreground of FIG. 2 and the reading area withhigh mean power 14 shown at the back. Steep gradients in mean power areevident, especially in the outlying regions 16.

[0010] Many progressive lens design systems permit the designer to setoptical properties at only a few isolated points, curves, or zones ofthe lens and employ a variety of interpolative methods to determine theshape and optical properties of the remainder of the lens.

[0011] U.S. Pat. No. 3,687,528 to Maitenaz, for example, describes atechnique in which the designer specifies the shape and opticalproperties of a base curve running from the upper part of the lens toits lower part. The base curve, or “meridian line” is the intersectionof the lens surface with the principal vertical meridian, a planedividing the lens into two symmetrical halves. The designer isconstrained by the requirement that astigmatism vanish everywhere alongthe meridian line (i.e. the meridian line must be “umbilical”). Maitenazdiscloses several explicit formulas for extrapolating the shape of thelens horizontally from an umbilical meridian.

[0012] U.S. Pat. No.4,315,673 to Guilino describes a method in whichmean power is specified along an umbilical meridian and provides anexplicit formula for extrapolating the shape of the remainder of thelens.

[0013] In a Jul. 20, 1982 essay, “The TRUVISION® Progressive PowerLens,” J. T. Winthrop describes a progressive lens design method inwhich the distance and reading zones are spherical. The design methoddescribed includes specifying mean power on the perimeters of thedistance and reading zones, which are treated as the only boundaries.

[0014] U.S. Pat. No.4,514,061 to Winthrop also describes a design systemin which the distance and reading areas are spherical. The designerspecifies mean power in the distance and reading areas, as well as alongan umbilical meridian connecting the two areas. The shape of theremainder of the lens is determined by extrapolation along a set oflevel surfaces of a solution of the Laplace equation subject to boundaryconditions at the distance and reading areas but not at the edge of thelens. The lens designer cannot specify lens height directly at the edgeof the lens.

[0015] U.S. Pat. No. 4,861,153 to Winthrop also describes a system inwhich the designer specifies mean power along an umbilical meridian.Again, the shape of the remainder of the lens is determined byextrapolation along a set of level surfaces of a solution of the Laplaceequation that intersect the umbilical meridian. No means is provided forthe lens designer to specify lens height directly at the edge of thelens.

[0016] U.S. Pat. No. 4,606,622 to Furter and G. Furter, “Zeiss GradalHS—The progressive addition lens with maximum wearing comfort”, ZeissInformation 97, 55-59, 1986, describe a method in which the lensdesigner specifies the mean power of the lens at a number of specialpoints in the progression corridor. The full surface shape is thenextrapolated using splines. The designer adjusts the mean power at thespecial points in order to improve the overall properties of thegenerated surface.

[0017] U.S. Pat. No.5,886,766 to Kaga et al. describes a method in whichthe lens designer supplies only the “concept of the lens.” The designconcept includes specifications such as the mean power in the distancezone, the addition power, and an overall approximate shape of the lenssurface. Rather than being specified directly by the designer, thedistribution of mean power over the remainder of the lens surface issubsequently calculated.

[0018] U.S. Pat. No. 4,838,675 to Barkan et al. describes a method forimproving a progressive lens whose shape has already been roughlydescribed by a base surface function. An improved progressive lens iscalculated by selecting a function defined over some subregion of thelens, where the selected function is to be added to the base surfacefunction. The selected function is chosen from a family of functionsinterrelated by one or a few parameters; and the optimal selection ismade by extremizing the value of a predefined measure of merit.

[0019] In a system described by J. Loos, G. Greiner and H. P. Seidel, “Avariational approach to progressive lens design”, Computer Aided Design30, 595-602, 1998 and by M. Tazeroualti, “Designing a progressive lens”,in the book edited by P. J. Laurent et al., Curves and Surfaces inGeometric Design, A K Peters, 1994, pp. 467-474, the lens surface isdefined by a linear combination of spline functions. The coefficients ofthe spline functions are calculated to minimize the cost function. Thisdesign system does not impose boundary conditions on the surface, andtherefore lenses requiring a specific lens edge height profile cannot bedesigned using this method.

[0020] U.S. Pat. No.6,302,540 to Katzman et al. discloses a lens designsystem that requires the designer to specify a curvature-dependent costfunction. In the Katzman system, the disk of the lens is preferablypartitioned into triangles. The system generates a lens surface shapethat is a linear combination of independent “shape polynomials,” ofwhich there are at least seven times as many as there are partitioningtriangles (8:17-40). The surface shape generated approximately minimizea cost function that depends nonlinearly on the coefficients of theshape polynomials (10:21-50). Calculating the coefficients requiresinverting repeatedly matrices of size equal to the number ofcoefficients. Since every shape polynomial contributes to the surfaceshape over every triangle, in general none of the matrices' elementsvanishes. As a result, inverting the matrices and calculating thecoefficients take time proportional to at least the second power of thenumber of shape polynomials.

[0021] The inherent inaccuracy of the shape polynomials (10:10-14)implies that the disk must be partitioned more finely wherever the meanpower varies more rapidly. These considerations set a lower limit on thenumber of shape polynomial coefficients that would have to becalculated, and hence the time the system would need to calculate thelens surface shape. Since the Katzman system requires time that is atleast quadratic in the number of triangles to calculate the lenssurface, the system is inherently too slow to return a calculated lenssurface to the designer quickly enough for the designer to workinteractively with the system. The inherent processing delay preventsthe designer from being able to create a lens design and then makeadjustments to the design while observing the effects of the adjustmentsin real-time.

[0022] None of the above design systems provides a simple method bywhich the lens designer can specify the desired optical properties overthe entire surface of the lens and derive a design consistent with thoseoptical properties. As a consequence, many of these prior systems resultin optical defects in the outlying regions of the lens and unnecessarilysteep gradients in mean power. Furthermore, the computational complexityof some of the prior systems result in a lengthy design process thatdoes not permit the lens designer to design the lens interactively. Manyof the prior systems also do not include a definition of the lens heightaround the periphery of the lens and therefore do not maximize theuseful area of the lens.

BRIEF SUMMARY OF THE INVENTION

[0023] The present invention seeks to provide the lens designer with ameans to specify as parameters both the mean power of the lens over itsentire surface and the height of the lens around its boundary and toobtain the surface shape of the lens consistent with those parameters intime short enough for the designer to make use of interactively. Lensdesigns can be created which have smooth, continuous optical propertiesdesirable for wearer comfort, ease of adaptation, and maximizing theeffective usable area of the lens.

[0024] The present invention differs from previous design processeswhich generally start by modeling the lens surface shape directly,calculating optical properties, and then attempting to modify thesurface shape so as to optimize optical properties. The prior artprocess of varying surface shape to achieve desired optical propertiesis unstable numerically. For this reason, previous design processescannot be relied upon to generate lens designs quickly enough for thedesigner to use interactively. In contrast to previous design processes,the present invention starts with a prescription of the key opticalproperty of mean power over the lens surface, together with the lensedge height, and then calculates the lens surface shape.

[0025] In accordance with the invention, mean power is specified at aplurality of points distributed over the entire surface of the lens andlens height is specified around the edge of the lens. Lens height isdetermined at the plurality of points consistent with the specified meanpower and the lens edge height in part by finding a unique solution to apartial differential equation of the elliptic type subject to the lensedge height as a boundary condition.

[0026] The present invention preferably incorporates a method forredistributing astigmatism in the lens design. The method redistributesastigmatism more evenly over the surface of the lens and reduces peaksof astigmatism in critical areas. The present invention preferably alsoincorporates a method of creating special lens designs for left andright eyes whilst maintaining horizontal symmetry and prism balance.

[0027] The method of the present invention is preferably implementedusing software executing on a computer to provide a system to define alens surface shape in an interactive manner with smooth, continuousoptical properties desirable for wearer comfort, ease of adaptation, andmaximum effective use of the lens area.

[0028] The invention also comprises a progressive lens designedaccording to the disclosed design method. Preferred embodiments of alens include a progressive lens having a distance area and a readingarea wherein mean power over the lens surface varies according to a setof curves forming iso-mean power contours on the lens surface and acontour defining an area of constant mean power in the distance area isan ellipse with a ratio of major axis to minor axis in the range ofabout 1.1 to 3.0. Another preferred embodiment of a lens includes adistance area having a first mean power, a reading area having a secondmean power higher than the first mean power, and a central area betweenthe distance and reading areas with a width of at least about 10millimeters wide and in which mean power increases smoothly andsubstantially monotonically throughout the central area in a directionfrom the distance area to the reading area.

[0029] The invention also comprises a system for designing progressivelens comprising a processor for accepting inputs defining mean powervariation over a coordinate system covering the surface of the lens anddefining lens height around the edge of the lens and for calculatinglens height at a plurality of points over the lens surface by solving anelliptic partial differential equation subject to the lens height at theedge of the lens as a boundary condition, and a memory for storing thecalculated lens height values. The lens design created using the systemof the present invention is preferably manufactured using a CNCcontrolled grinding or milling machine using techniques well known inthe art.

[0030] Further aspects of the invention are described hereinafter.

BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The following is a description of certain embodiments of theinvention, given by way of example only and with reference to thefollowing drawings, in which:

[0032]FIG. 1 is a diagram of a conventional progressive lens, shown invertical elevation.

[0033]FIG. 2 is a three dimensional representation of the mean powerdistribution over the surface of a typical prior art progressive lens.

[0034]FIG. 3 is a diagram of a lens according to an embodiment of thecurrent invention in vertical elevation view showing a connecting pathand a representative subset of a system of contours intersecting theconnecting path.

[0035]FIG. 4 is a graph showing an example of a function specifying meanpower along the connecting path.

[0036]FIG. 5 is a vertical elevation view of the surface of a lensshowing a preferred coordinate system comprising x- and y-axes and angleθ.

[0037]FIG. 6 is a vertical elevation view of the surface of a lensaccording to an embodiment of the current invention showing the boundaryareas of the lens.

[0038]FIG. 7 is a graph showing an example of a lens boundary heightfunction ranging from θ=0 to 360 degrees around the lens boundary.

[0039]FIG. 8 is a three dimensional representation of a theoretical meanpower distribution over the surface of a lens according to an embodimentof the present invention.

[0040]FIG. 9 is a graph showing an example of optimizing the mean powerprofile along the connecting path.

[0041]FIG. 10 is a vertical elevation view of the surface of a lensshowing an example of mean power distribution over a family of iso-meanpower ellipses.

[0042]FIG. 11 is a graph showing an example of an edge height profilearound the periphery of a lens.

[0043]FIG. 12 is a vertical elevation view of the surface of a lensshowing an example of the distribution of astigmatism resulting from themean power distribution of FIG. 10 and edge height profile of FIG. 11.

[0044]FIG. 13 is a vertical elevation view of the surface of a lensshowing an example of altered mean power distribution to reduceastigmatism along the centerline.

[0045]FIG. 14 is a graph showing an example of an altered edge heightprofile.

[0046]FIG. 15 is a vertical elevation view of the surface of a lensshowing an example of the redistribution of astigmatism resulting fromthe altered mean power distribution of FIG. 13 and altered edge heightprofile of FIG. 14.

[0047]FIG. 16 is a vertical elevation view of the surface of a lensshowing an example of a mean power distribution incorporating the changein mean power profile along the connecting path as shown in FIG. 17.

[0048]FIG. 17 is a graph showing an example of change in the mean powerprofile along the connecting path to optimize the mean power in thecentral corridor area.

[0049]FIG. 18 is a vertical elevation view of the surface of a lensshowing an example of an astigmatism distribution derived from therecalculated surface height distribution.

[0050]FIG. 19 is a vertical elevation view of the surface of a lensshowing an example of a rotated mean power distribution.

[0051]FIG. 20 is a graph showing an example of a rotated edge heightprofile.

[0052]FIG. 21 is a vertical elevation view of the surface of a lensshowing an example of astigmatism distribution resulting from therotated mean power distribution of FIG. 19 and rotated edge heightprofile of FIG. 20.

[0053]FIG. 22 is a flowchart showing the major steps of one embodimentof the design method of the present invention.

DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

[0054] Certain embodiments of the invention will now be described, byway of example only, to illustrate the subject matter of the invention.The surface of a lens may be described by the equation z=f(x, y), wherex, y, and z are rectangular Cartesian co-ordinates.

[0055] For brevity let${\partial_{x}{\equiv \frac{\partial}{\partial x}}};{\partial_{y}{\equiv \frac{\partial}{\partial y}}};{\partial_{x}^{2}{\equiv \frac{\partial^{2}}{\partial x^{2}}}};{\partial_{y}^{2}{\equiv \frac{\partial^{2}}{\partial y^{2}}}};{{{and}\quad \partial_{xy}^{2}} \equiv {\frac{\partial^{2}}{{\partial x}{\partial y}}.}}$

[0056] principal radii of curvature R₁ and R₂ of the surface are theroots of the quadratic equation:

└rt−s ² ]R ² +h[2pqs−(1+p ²)t−(1+q ²)r┘R+h ⁴=0   (1)

[0057] where p≡∂_(x)z, q≡∂_(y)z, r≡∂_(x) ²z, s≡∂_(xy) ²z, t≡∂_(y) ²z and$h \equiv {\sqrt{\left( {1 + p^{2} + q^{2}} \right)}.}$

[0058] See, e.g., I. N. Bronshtein & K. A. Semendyayev, “A Guide Book toMathematics,” Verlag Harri Deutsch, 1971, hereby incorporated byreference in its entirety.

[0059] The principal values of curvature are 1/R₁ and 1/R₂ respectively.The principal curvature difference${\langle\delta\rangle} \equiv {{\frac{1}{R_{1}} - \frac{1}{R_{2}}}}$

[0060] is related to the optical property of astigmatism (also known ascylinder power) by D=1000(n−1)<δ> where D is measured in diopters, n isthe refractive index, and distance is measured in millimeters.

[0061] The mean curvature${\langle\mu\rangle} \equiv {\frac{1}{2}\left( {\frac{1}{R_{1}} + \frac{1}{R_{2}}} \right)}$

[0062] is similarly related to the optical property of mean powerM=1000(n−1)<μ> also measured in diopters. As used herein, <μ> is themean of the two principal curvatures, and <δ> is the absolute differenceof the two principal curvatures.

[0063] In one embodiment of the present invention, the designerpreferably prescribes M(x, y) and thus <μ>(x,y) over the entire lensarea. For designing a progressive lens, mean power is prescribed overthe entire lens surface using a preferred system of coordinates. Thispreferred system consists of a continuous set of non-mutuallyintersecting contours that collectively fill the entire area of the lensand a connecting path, with each contour line intersecting theconnecting path once. The connecting path is a curve connecting a pointin the distance area to one in the reading area. To specify the meanpower in this preferred system of coordinates, the designer specifieshow mean power varies along the connecting path and how mean powervaries along each contour from its point of intersection with theconnecting path. Preferably, variation in mean power along theconnecting path should be described by a suitably smooth functionranging from a lower value in the distance area to a higher value in thereading area.

[0064] It is also preferred that lens height around the boundary bespecified by a function that varies little near the distance and readingareas and gradually near the intermediate regions shown in FIG. 6. Oneway to construct such a function is as a smooth, piecewise composite ofany of a wide variety of well-known elementary functions, such aspolynomial, trigonometric, or gaussian functions.

[0065] The lens surface shape is then determined on the basis of themean power distribution and lens height at the boundary. The preferredmethod is to solve a boundary value problem.

[0066] Unwanted astigmatism in critical areas may then be reduced andindividual left and right lens designs may be created, as described inmore detail below.

[0067] A. Prescribing Mean Power Over the Lens Surface

[0068] For a progressive lens of the present invention, a preferredmethod for prescribing the mean power M as a function over the entirelens area involves four steps. First, the designer selects points, P_(D)in the distance area and P_(R) in the reading area, and a pathconnecting those points. In one embodiment, both of the points and theconnecting path lie along the left-right symmetry axis of the lens.Therefore in this embodiment the connecting path is referred to as thepower profile meridian. FIG. 3 is a vertical elevation (plan view) of aprogressive lens showing the selected points P_(D) and P_(R) shown asendpoints 20 and 22 at each end of connecting path (or power profilemeridian) 24.

[0069] Second, a continuous set of contours is selected, subject to theconditions that each contour in the set intersects the power profilemeridian once and no two contours in the set intersect one another. Thecurves in FIG. 3 within the lens boundary 10 are representative membersof one example of such a continuous set of contours. In one preferredembodiment, the set of contours collectively fill the entire disk of thelens. In a second preferred embodiment, the designer may define adistance area 32 and reading area 34 of constant mean power. The set ofcontours collectively fill the remaining lens area. In the example shownin FIG. 3, curves 28 and 30 are contours that form the boundaries of theareas of constant mean power. In this example, the continuous set ofcontours consists of two families of hyperbolae: $\begin{matrix}{{\frac{x^{2}}{\xi_{R}^{2}} - \frac{\left( {y - P_{R}} \right)^{2}}{_{R}^{2}}} = {{1\quad {for}\quad y} \leq {0\quad {and}}}} & \left( {2A} \right)\end{matrix}$

$\begin{matrix}{{{{\frac{x^{2}}{\xi_{D}^{2}} - \frac{\left( {y - P_{D}} \right)^{2}}{_{D}^{2}}} = {{1\quad {for}\quad y} \geq 0}},}\quad} & \left( {2B} \right)\end{matrix}$

[0070] where the x and y coordinates are defined according thecoordinate system as shown in FIG. 5. As the parameters ζ_(r) and ζ_(D)vary, the set of contours fill the entire area between contours 28 and30. For y=0, the two families of hyperbolae overlap, each including theequator 26 of the disk as a member when ξ_(D) or ξ_(R) is varied.

[0071] The set of contour lines illustrated in FIG. 3 is by no means anunique example of contours that can fulfill the conditions given above.Contours may be selected from families of curves other than conics, andfrom families of conics other than hyperbolae. In the second preferredembodiment, the set of contours could equally well consist of twofamilies of ellipses. In one example of this embodiment, the contourforming the boundary of the distance area is preferably an ellipse witha ratio of major axis to minor axis in the range of about 1.1 to 3.0. Itis also expected that contours may be selected from families of curvesother than conics.

[0072] In a third step of a preferred method for prescribing the meanpower over the lens, the designer prescribes a function specifying thevariation in mean power along the power profile meridian. Preferably,the prescribed function takes into account criteria of wearer comfortand the intended use of the lens. Functions that meet such criteria may,for example, be linear combinations of elementary functions. One exampleof such a function is:${M(y)} = {M_{D} + {\left\lbrack \frac{M_{R} - M_{D}}{2} \right\rbrack \left\lbrack {1 - {\cos \left( {\pi \frac{y_{D} - y}{y_{D} - y_{R}}} \right)}} \right\rbrack}}$

[0073] where M_(D) is mean power specified at a point P_(D)=(0,y_(D)) inthe distance area and M_(R) is mean power specified at a pointP_(R)=(0,y_(R)) in the reading area.

[0074]FIG. 4 is a graph of mean power M plotted against the y-axis ofthe lens along the length of the power profile meridian. The ends of thegraph correspond to the endpoints 20 and 22 of the power profilemeridian. A function 36 specifying mean power M along the power profilemeridian is shown as an example of a suitable variation of mean power.In the example shown, mean power is constant in the distance area 32 andreading area 34.

[0075] Finally, in the fourth step of a preferred method for prescribingthe mean power over the lens, the designer prescribes functionsspecifying the variation in mean power M along each of the contourlines. The mean power at the point where a contour intersects the powerprofile meridian equals the mean power specified at that point on thepower profile meridian. Thus, defining the variation in mean power Malong each of the contour lines completes the definition of mean powerover the entire surface of the lens. One convenient choice consistentwith this requirement is for mean power simply to remain constant alongeach contour. Other choices are also compatible with the disclosedembodiment.

[0076] B. Prescribing Lens Height at the Lens Boundary

[0077] In a preferred embodiment, the designer also prescribes the lensheight at the edge of the lens. (As used herein, the terms “lens edge”and “lens boundary” are synonymous). The designer specifies a lensboundary height function z(θ) where z denotes the height of the lens andθ denotes the angular coordinate around the boundary of the lens. FIG. 5illustrates the preferred convention for θ to be defined as the anglearound the edge 48 of the lens in an anticlockwise direction starting atthe x-intercept of the edge of the lens.

[0078] Preferably, the designer's specification of z(θ) takes intoaccount criteria of wearer comfort and the intended use of the lens.Discontinuities or abrupt changes in z(θ) generally lead to image jumpsthat are uncomfortable for the wearer. Also, to be supported in aneyeglass frame a lens should be neither too thick nor too thin aroundits edge.

[0079] For a progressive lens, additional design criteria preferablyapply to z(θ). FIG. 6, a vertical elevation (plan view) of the surfaceof a progressive lens, illustrates segments of the lens boundary thatcorrespond roughly to adjoining areas of a typical progressive lens,illustrated in FIG. 1. Boundary segment 50 roughly adjoins distance area40;

[0080] boundary segment 52 roughly adjoins reading area 42; and theboundary segments 54 and 56 roughly adjoin the outlying regions 44 and46. To facilitate designs with relatively uniform optical properties inthe distance and reading areas, it is preferred that z(θ) vary littlewithin each of segments 50 and 52. To facilitate designs that do notproduce uncomfortable image distortions at the lens periphery, it ispreferred that in segments 54 and 56, z(θ) vary gradually so as to makesubstantially smooth transitions between segments 50 and 52. In order tofulfill these design criteria the designer may, for example, constructz(θ) from a smooth, piecewise composite of any of a wide variety ofwell-known elementary functions, such as polynomial or trigonometricfunctions.

[0081]FIG. 7 illustrates the preferred qualitative behavior of the lensboundary height function 60, showing lens boundary height z on thevertical axis plotted against angular coordinate θ on the horizontalaxis, with θ varying from 0 to 360 degrees over lens boundary segments50, 52, 54, and 56.

[0082] Within these criteria, some flexibility remains in thespecification of z(θ) for a progressive lens. After examining theoptical properties of a lens whose surface shape has been determinedaccording to the present embodiment, a designer may exploit thisflexibility by modifying z(θ). It has been shown that a typicalprogressive lens can be designed and optimized using the methodsdescribed herein in an hour or less, with each successive calculation oflens height distribution over the surface of the lens being performed ina matter of minutes. With the benefit of such rapid feedback, thedesigner may modify z(θ) in a way that leads to improved opticalproperties, such as lowered astigmatism, in critical areas of the lens.

[0083] C. Determining the Lens Surface Shape

[0084] When the mean curvature function <μ> is specified, the heightfunction satisfies: $\begin{matrix}{{\left\lfloor {\partial_{x}^{2}{+ \partial_{y}^{2}}} \right\rbrack z} = F} & (3)\end{matrix}$

[0085] where

F=2<μ>[1+(∂_(x) z)²+(∂_(y) z)²]^(3/2)−[∂_(y) z] ²∂_(x) ² z+2[(∂_(x)z)(∂_(y) z)]∂_(xy) ² z−[∂ _(x) z] ²∂_(y) ² z

[0086] The present embodiment determines the lens surface shape bysolving equation (3) subject to the boundary condition that the lensedge height z(θ) is specified. Since equation (3) is a partialdifferential equation of the elliptic type, a unique, stable solutionfor the lens surface shape z must exist. To determine that solution, thepresent embodiment uses an iterative process to solve equation (3)numerically.

[0087] To establish a starting solution, a low power lens configuration,in which |∂_(x)z|<<1 and |∂_(y)z|<<1, is assumed. For this startingsolution, ∂_(x)z, and ∂_(y)z may be eliminated from equation (3),leading to a Poisson equation: $\begin{matrix}{{\left\lfloor {\partial_{x}^{2}{+ \partial_{y}^{2}}} \right\rfloor z} = {2{\langle\mu\rangle}}} & (4)\end{matrix}$

[0088] The area of the lens is covered with a square mesh. Meancurvature <μ> is evaluated from M at mesh points; its values areproportional to F⁽⁰⁾, a function of two discrete variables. Throughout,a function with a superscript in parentheses will be the function of twodiscrete variables representing the values at mesh points of thecorresponding continuum function. z⁽⁰⁾ at mesh points on the boundary ofthe disk represents values of z(θ) at those points. For mesh points nearthe boundary of the disk, the value of z⁽⁰⁾ is a suitable average ofnearby values of z(θ). Elsewhere on the mesh, z⁽⁰⁾ need not be defined.

[0089] Superscripts in parentheses refer to the stage of the iteration.In the first iteration, the discrete analog of equation (4):$\begin{matrix}{{\left( {\partial_{x}^{2}z} \right)^{(1)} + \left( {\partial_{y}^{2}z} \right)^{(1)}} = {{F^{(0)}\quad {with}\quad F^{(0)}} = {2{\langle\mu\rangle}}}} & (5)\end{matrix}$

[0090] is solved to obtain z⁽¹⁾. z⁽¹⁾ is solved for at mesh points usingthe Successive Over-Relaxation (SOR) Technique. The SOR technique forsolving elliptic equations is discussed in W. H. Press et al.,“Numerical Recipes in C: The Art of Scientific Computing” (CambridgeUniversity Press 1992) at sections 19.2 and 19.5, which are herebyincorporated by reference.

[0091] In subsequent iterations, equation (6), the discrete analog ofequation (3) $\begin{matrix}{{\left( {\partial_{x}^{2}\quad z} \right)^{({n + 1})} + \left( {\partial_{y}^{2}\quad z} \right)^{({n + 1})}} = F^{(n)}} & (6)\end{matrix}$

[0092] is solved to obtain z^((n+1)). For n≧1, F^((n)) includes all theterms shown in equation (3).

[0093] The values of F^((n)) are calculated at mesh points using thevalues of z^((n)) determined at mesh points in the previous iteration.The partial differentials of z that appear in F, as shown in equation(3), are calculated using central difference schemes, with special carebeing taken for mesh points near the circular boundary. Again, the SORtechnique is used to solve for z^((n+1)) at mesh points.

[0094] The SOR technique employs a repetitive series of sweeps over themesh to converge on a solution. The rate of convergence is dependent onthe value of the Over-Relaxation Factor (ORF), and a preferred value ofthe ORF is determined experimentally. Once determined, the same ORFvalue is also preferred for solving similar equations, such assuccessive iterations of equation (6). (See Press et al., at section19.5)

[0095] An important advantage of the SOR technique is that it reachesconvergence in a time proportional to the square root of the number ofmesh points. This feature implies that at modest cost in computationaltime, a sufficient mesh density can be implemented for SOR to convergeto the solution of equation (6) that corresponds at mesh points to theunique solution of equation (3).

[0096] It has been found that five iterations of equation (6) willtypically produce a satisfactory numerical solution of equation (3).

[0097] D. Reducing Unwanted Astigmatism in Critical Areas

[0098] Using the lens surface shape resulting from step C above,principal curvature difference <δ> can be calculated at every meshpoint. Partial differentials of z that appear in <δ> are calculatedusing central difference schemes, with special care being taken for meshpoints near the circular boundary.

[0099] Excessive astigmatism may be found in critical areas such as thecentral and reading areas. While astigmatism cannot be avoided entirelyin a progressive lens design, astigmatism can be redistributed moreevenly, away from critical areas.

[0100] Astigmatism in the central area, for example, can be reduced toimprove optical performance there. A criterion for the maximum level ofastigmatism acceptable in the central area, such asD≦0.15*(M_(R)−M_(D)), could be imposed. Here, M_(D) is mean powerspecified at point P_(D) in the distance area and M_(R) is mean powerspecified at point P_(R) in the reading area.

[0101] Assume that the lens shape is symmetrical about the centerline,so that z=f(x, y) with f(−x, y)=f(x, y). Then along the centerline, p=0and s=0 and the mean curvature <μ> and principal curvature difference<δ> are respectively given by equation (7): $\begin{matrix}{\begin{matrix}{{\langle\mu\rangle} = \frac{\left( {t + {h^{2}r}} \right)}{2h^{3}}} & \quad & {and} & \quad & {{\langle\delta\rangle} = \frac{\left( {t - {h^{2}r}} \right)}{h^{3}}}\end{matrix}\quad.} & (7)\end{matrix}$

[0102] To make astigmatism D vanish exactly along the centerline, itwould be necessary for t to be made equal to h²r and mean curvature <μ>made equal to r/h. Therefore the <μ> function would have to be modifiedaccording to equation (8):

<μ>(0,y)→<μ>(0,y)+Δ<μ>(0,y)   (8)

[0103] where $\begin{matrix}{\left. {{\Delta {\langle\mu\rangle}\left( {0,y} \right)} \equiv \frac{r}{h}} \middle| {}_{({0,y})}{{- {\langle\mu\rangle}}\left( {0,y} \right)} \right. = \left. \frac{\partial_{x}^{2}\quad z}{\sqrt{1 + \left( {\partial_{y}\quad z} \right)^{2}}} \middle| {}_{({0,h})}{{- {\langle\mu\rangle}}\left( {0,y} \right)} \right.} & (9)\end{matrix}$

[0104] To reduce astigmatism D in the central area and at the same timedistribute changes in mean power M across the lens, a spreading functionσ(x) can be employed:

<μ>(x,y)→<μ>(x,y)+σ(x)Δ<μ>(0,y)   (10)

[0105] σ(x) may be any smoothly-varying function that takes the value 1at x=0. One example of such a function is: $\begin{matrix}{{\sigma (x)} = \begin{Bmatrix}{\exp \left( {- {k^{2}\left( {x - x_{L}} \right)}^{2}} \right)} & \left| {x < x_{L}} \right. \\{\exp \left( {- {k^{2}\left( {x - x_{R}} \right)}^{2}} \right)} & \left| {x > x_{R}} \right. \\1 & \left| {x_{L} \leq x \leq x_{R}} \right.\end{Bmatrix}} & (11)\end{matrix}$

[0106] where x_(R) and −x_(L) take equal values prior to handing andcreate a constant region for the spreading function σ(x). The parameterk controls the rate of decay of σ(x) to the left and to the right of theconstant region. The mean curvature function <μ>(x,y) resulting fromequations (8), (9) and (10) can be calculated at mesh points and is usedto completely recalculate the surface height function z in the mannerdescribed in step C.

[0107] In the complete recalculation of z with a selected σ(x), thederivatives involved in equation (9) will of course in general adopt newvalues. As a result, the mean curvature function <μ>(x, y) will alsoadopt new values. The variables z, <μ>, and <δ> are recalculatedrepeatedly, with repetition halting at the discretion of the designer.If necessary the values of x_(L), x_(R), and k can themselves be changedduring this process.

[0108] Astigmatism can be reduced similarly in any critical area, firstby determining the local change in M required to make D vanish exactlyin the area, and then by distributing the change in M across the lens.The result is a set of modified values of M at mesh points. The modifiedM is plugged back into step C at equation (5) to obtain a modified lenssurface function z at mesh points. The modified z, in turn, is used torecalculate the astigmatism D at mesh points, and the whole process maybe repeated until the distribution of astigmatism is found acceptable.

[0109] E. Optimizing the Mean Power Distribution Around the PowerProfile Meridian

[0110] As a result of changing the mean power to reduce unwantedastigmatism, it may be found that the mean power in certain criticalareas is no longer what the designer desires. FIG. 9 shows an example ofa mean power profile after reducing the astigmatism (line 72). For atypical design, it will be desired to maintain the mean power below acertain value at the fit point (line 74). It will also be desired forthe mean power to reach the correct addition power, in this example 2.00diopters, at the addition measuring point (line 76). To achieve thedesired mean power profile, without raising the astigmatism levelssignificantly, the mean power can be altered locally. This is shown byline 70 in FIG. 9, and this alteration is made over some limited widthin the x direction of, for example, 12 to 16 mm. The modified mean canbe distributed across the lens in a simple linear fashion. The new Mdistribution is plugged back into step C at equation (5) to obtain amodified lens surface function z at mesh points. The modified z, inturn, is used to recalculate the astigmatism D at mesh points, so thatit can be checked to be within acceptable limits. The whole process maybe repeated until the distribution of mean and astigmatism is foundacceptable.

[0111] F. Designing Left and Right Lenses

[0112] Once an acceptable lens shape has been obtained, right-hand andleft-hand versions are designed in order to minimize binocularimbalance. Contrary to previous approaches to the handing problem, thedirect control of handing mechanics resides in the mean curvature andedge height prescriptions. In order to accomplish this handed lenses aredesigned by rotating both the mean curvature <μ>(x, y) and the boundaryheight z(θ) in an angle-dependent manner. Specifically,

<μ>(ρ,θ)→<μ>(ρ,H(θ))   (12)

z(θ)→z(H(θ))   (13)

[0113] where (ρ,θ) are polar coordinates corresponding to (x, y). Thehanding function H is of the form: $\begin{matrix}{{H(\theta)} = {h_{0}\begin{Bmatrix}{\exp \left( {- {K^{2}\left( {\theta - \frac{3\quad \pi}{2} + \omega} \right)}^{2}} \right)} & \left| {\theta < {\frac{3\quad \pi}{2} - \omega}} \right. \\{\exp \left( {- {K^{2}\left( {\theta - \frac{3\quad \pi}{2} - \omega} \right)}^{2}} \right)} & \left| {\theta > {\frac{3\pi}{2} + \omega}} \right. \\1 & \left| {{\frac{3\quad \pi}{2} - \omega} \leq \theta \leq {\frac{3\quad \pi}{2} + \omega}} \right.\end{Bmatrix}}} & (14)\end{matrix}$

[0114] where h₀ is the handing angle, ω controls the undistorted portionof the handed reading region, and K determines the nature of the regionsahead of and behind the pure rotation. Typical values of theseparameters could be h₀=9 degrees, ω=30 degrees, and K=1.5. The meancurvatures and edge height values are plugged into step C at equation(5) to obtain a recalculated lens surface function z(x, y) at meshpoints.

[0115]FIG. 8 is a three dimensional representation of a theoretical meancurvature distribution over the surface of a lens according to anembodiment of the current invention. Mean curvature M is graphed in thevertical direction. M is graphed as a function of x and y, which areshown as the two horizontal directions. The disc of the lens is viewedfrom an angle less than 90° above the plane of the lens. Since thedistance area is shown in the foreground and the reading area at thebackground of FIG. 8, y increases in the background-to-foregrounddirection. As can be seen, there is a region of lesser mean curvature 62in the distance area and greater mean curvature 64 in the reading area.The mean power transitions smoothly and increases substantiallymonotonically with increasing y throughout the optically critical areabetween the distance area and the reading area as well as in theoutlying areas 66 and 68.

[0116] G. An Example Lens Design

[0117] The following is an example of a lens design produced usingmethods comprising the present invention. A mean power distribution isinitially defined for the complete surface of the lens. A suitabledistribution using a family of iso-mean power ellipses can be seen inFIG. 10, in which contour lines are shown having mean power valuesbetween 0.25 to 2.00 diopters in increments of 0.25 diopters. Tocompletely define the entire surface it is also necessary to specify thelens height around the edge of the lens. An example of a suitable lensedge height function is shown in FIG. 11. This figure shows the lenssurface height z in millimeters referenced from the edge of the distancearea. These parameters are used as inputs for equation (10), discussedabove in step C, and the equations are solved for the surface heights zover the complete surface. The solution is derived numerically using ahigh-speed digital computer, using software and programming techniqueswell known in the art. A suitable machine would be a personal computerwith a Pentium III or later processor, such as a Compaq EVO D300. Thecomputation time required to solve the boundary value problem isapproximately proportional to the square root of the number of points atwhich the height is calculated.

[0118] From the resultant z height values, the distribution ofastigmatism and sphere power can be calculated for the design. Althoughthe distribution of sphere power can in principle be calculated directlyfrom the defined mean power distribution and the calculated distributionof astigmatism, calculating the distribution of sphere power from theresultant z height values is useful to confirm that those z heightvalues are consistent with the defined mean power distribution. FIG. 12shows the distribution of astigmatism resulting from the mean powerdistribution and lens edge height function of FIG. 10 and FIG. 11.

[0119] The next step is to reduce the astigmatism in the centralcorridor area to an acceptable level. This reduction is achieved byalteration in the mean power distribution according to equations (8),(9) and (10) described above. The resulting altered mean powerdistribution is shown in FIG. 13. To take criteria of patient comfortinto account as is preferred, the lens edge height function may also bealtered, and an example of an altered lens edge height function is shownin FIG. 14. The altered mean power and edge height function are thenused to recalculate the distribution of surface heights z over thecomplete surface by solving equation (5) as before. An astigmatismdistribution derived from the recalculated surface height distributionis shown in FIG. 15. This step may be repeated until the designer findsthe astigmatism distribution acceptable.

[0120] An example of the changes caused in the mean power profile alongthe centerline to reduce astigmatism in the central corridor area isshown in FIG. 17. Having found that the astigmatism in the centralcorridor area has been reduced to acceptable levels, the designer mayfind that the mean power profile along the centerline no longer complieswith what was originally desired. As shown in FIG. 17 for example, inthe addition area, the mean power at the addition measurement point (−13mm) is below the desired 2.00 diopters. Then the mean power profile mustbe optimized according to step E above. The optimized mean power profileover a 12 mm width surrounding the centerline of the lens is then usedas input to recalculate the distribution of surface heights z by againsolving equation (5). A mean power distribution incorporating thechanges shown in FIG. 17, is shown in FIG. 16. The altered mean powerand the previous edge height profiles function are then used torecalculate the distribution of surface heights z over the completesurface by solving equation (5) as before and an astigmatismdistribution derived from the recalculated surface height distributionis shown in FIG. 18.

[0121] Finally the design has to be handed for use in a left or righteye of a spectacle frame. This is achieved by rotating both the meanpower distribution and lens edge height function as described in step Fabove and once again recalculating the distribution of surface heights zby solving equation (5) described above. An example of a rotated meanpower distribution is shown in FIG. 19 and an example of a rotated edgeheight function in shown in FIG. 20. After recalculating surface heightsz, the astigmatism distribution is again derived. An example of such anastigmatism distribution can be seen in FIG. 21.

[0122] As can be seen by FIG. 19, the completed lens design includes adistance area with relatively lower mean power in the top part of thelens and a reading area with relatively higher mean power in the bottompart of the lens. Throughout a central area that extends between thedistance and reading areas, mean power increases smoothly andsubstantially monotonically in the direction from the distance area tothe reading area. In a preferred embodiment, this central area is atleast 30 millimeters wide, but may vary about this width according tothe lens design. In some designs the minimum width of the centralportion may be about 20 millimeters wide, or may be about 10 millimeterswide.

[0123] The resulting distribution of surface heights z can then be usedin any of the following ways:

[0124] a. To directly machine the progressive surface onto a plastic orglass lens;

[0125] b. To directly machine a glass or metal mould which will be usedto produce a progressive plastic lens by either casting or molding; or

[0126] c. To machine a ceramic former in either a convex form which willbe used to produce a glass progressive lens by a slumping process, or aconcave form which will be used to produce a glass mould by a slumpingprocess from which a plastic progressive lens can be cast.

[0127] As discussed above, the calculation of the surface heights z ispreferably performed on a computer. The resulting data representing thedistribution of surface heights is preferably stored in the computer'smemory, and may be saved to a hard disk drive, CD-ROM, magnetic tape, orother suitable recording medium.

[0128] The machining is preferably performed by electronicallytransmitting the surface height data to a computernumerically-controlled (CNC) milling or grinding machine. Examples ofsuitable CNC machines include a Schneider HSC 100 CNC to directlymachine the progressive surface onto a plastic or glass lens, a MikronVCP600 to machine a glass or metal mould, and a Mikron WF32C orSchneider HSG 100 CNC to machine a ceramic former, although othersuitable machines are well known to those of skill in the art.

[0129] In each of the above cases the distribution of surface heights zmust be post-processed to suit the particular CNC controller on thegrinding/milling machine used. Compensation must also be built in to thesurface geometry depending on the size and type of grinding tool/cutterused to ensure that the design surface is produced. In the case ofmachining ceramic formers for use with a slumping process, furthercompensation must be built into the distribution of surface heights z totake care of unwanted geometry changes. These result from the bendingand flowing of the glass as it is heated up to its softeningtemperature, to allow it to take up the shape of the ceramic former.

[0130] Lenses produced according to the present invention need not havea circular outline. As part of any of the above manufacturingprocedures, lenses may be glazed into a variety of outlines for avariety of spectacle frames. Furthermore, the lens edge height used inthe calculation of lens surface heights z need not be the physical edgeof the lens blank. For example, a typical 70 millimeter circular lensblank may have edge heights defined 10 millimeters in from the actualedge of the lens blank, depending on the size of the lens ultimatelyrequired. In this example, the designer's specification of mean powerand the calculation of lens surface heights z will apply for the lensarea within the boundary at which lens edge height is defined, ratherthan for the entire surface of the lens blank.

[0131] A flow chart showing the process described above is provided inFIG. 22. The flowchart illustrates each of the main steps involved inthe design and manufacturing process for a progressive lens as describedabove. It should be noted that FIG. 22 describes only one example of adesign and manufacturing process and not all of the steps shown in theflow chart may be necessary for a given lens design.

[0132] Thus an improved method for designing progressive addition powerophthalmic lenses has been described. It will be appreciated that themethod has been described in terms of several embodiments, which aresusceptible to various modifications and alternative forms. Accordingly,although specific embodiments have been described, these are examplesonly and are not limiting upon the scope of the invention.

What is claimed is:
 1. A method for designing a progressive lens surfacecomprising: specifying mean power at a plurality of points distributedover the entire surface of the lens; specifying lens height around theedge of the lens; and determining lens height at the plurality of pointsconsistent with the specified mean power and lens edge height,comprising finding a unique solution of a partial differential equationof the elliptic type subject to a boundary condition of the lens edgeheight.
 2. The method of claim 1, wherein finding the unique solution ofthe partial differential equation comprises: employing a successiveover-relaxation technique to converge on the solution; and determiningan over-relaxation factor to most efficiently relax the equation.
 3. Themethod of claim 2, wherein the step of determining the lens height at aplurality of points comprises: defining a mesh comprising a plurality ofpoints over the surface of the lens; determining mean power at eachpoint on the mesh as defined by the specified mean power distributionover the lens surface; and numerically solving on the mesh a partialdifferential equation of the elliptic type, subject to the lens edgeheight as a boundary condition, to determine the lens height at eachpoint of the mesh.
 4. The method of claim 3, wherein the lens comprisesa distance area and a reading area, and wherein the step of specifyingmean power further comprises: specifying mean power along a connectingpath extending from a first point in the distance area to a second pointin the reading area; and specifying mean power over a coordinate systemdistributed over the surface of the lens consistently with the meanpower specified along the connecting path.
 5. The method of claim 4,wherein the coordinate system comprises a set of contour lines, eachcontour line intersecting the connecting path, and wherein specifyingmean power over the coordinate system further comprises specifying meanpower variation along the contour lines as a function, the mean power ona contour line and the mean power on the connecting path being equal atevery point where a contour line intersects the connecting path.
 6. Themethod of claim 5, further comprising rotating in a controlled mannerthe specified mean power values with respect to the plurality of pointsdistributed over the lens surface and the specified lens edge heightwith respect to the edge of the lens.
 7. The method of claim 1, whereinthe step of determining the lens height at a plurality of pointscomprises: defining a mesh comprising a plurality of points over thesurface of the lens; determining mean power at each point on the mesh asdefined by the specified mean power distribution over the lens surface;and numerically solving on the mesh a partial differential equation ofthe elliptic type, subject to the lens edge height as a boundarycondition, to determine the lens height at each point of the mesh. 8.The method of claim 7, wherein the lens comprises a distance area and areading area, and wherein the step of specifying mean power furthercomprises: specifying mean power along a connecting path extending froma first point in the distance area to a second point in the readingarea; and specifying mean power over a coordinate system widelydistributed over the entire area of the lens consistently with the meanpower specified along the connecting path.
 9. The method of claim 8,wherein the coordinate system comprises a set of contour lines, eachcontour line intersecting the connecting path, and wherein specifyingmean power over the coordinate system further comprises specifying meanpower variation along the contour lines as a function, the mean power ona contour line and the mean power on the connecting path being equal atevery point where a contour line intersects the connecting path.
 10. Themethod of claim 9, further comprising rotating in a controlled mannerthe specified mean power values with respect to the plurality of pointsdistributed over the lens surface and the specified lens edge heightwith respect to the edge of the lens.
 11. The method of claim 1, whereinthe lens comprises a distance area and a reading area, and wherein thestep of specifying mean power further comprises: specifying mean poweralong a connecting path extending from a first point in the distancearea to a second point in the reading area; and specifying mean powerover a coordinate system distributed over the surface of the lensconsistently with the mean power specified along the connecting path.12. The method of claim 11, wherein the step of specifying mean powerover the coordinate system further comprises: specifying mean power inthe distance area and reading area; and specifying mean power over acoordinate system distributed over the remaining area of the lensconsistently with the mean power specified along the connecting path.13. The method of claim 11, wherein the coordinate system comprises aset of contour lines, each contour line intersecting the connectingpath, and wherein specifying mean power over the coordinate systemfurther comprises specifying mean power variation along the contourlines as a function, the mean power on a contour line and the mean poweron the connecting path being equal at every point where a contour lineintersects the connecting path.
 14. The method of claim 13, wherein eachcontour line intersects the connecting path only once and each contourline does not intersect any other contour line.
 15. The method of claim14, wherein the mean power is constant along the length of each contourline.
 16. The method of claim 14, wherein the mean power varies alongthe length of each contour line.
 17. The method of claim 11, whereinspecifying the lens height around the edge of the lens comprisesdefining a boundary height profile function in which the boundary heightvaries only slightly in a first boundary segment adjacent to thedistance area and a second boundary segment adjacent to the readingarea, and the boundary height undergoes substantially smooth transitionsbetween the first and second boundary segments.
 18. The method of claim11, further comprising redistributing astigmatism away from theconnecting path.
 19. The method of claim 18, wherein the step ofredistributing astigmatism comprises: determining a change in mean powerrequired to reduce astigmatism on the connecting path; distributing thechange in mean power across the lens to modify the specified mean powervalues; determining lens height at the points of the plurality of pointsdistributed over the lens surface using the modified mean power valuesat the points.
 20. The method of claim 1, further comprising rotating ina controlled manner the specified mean power values with respect to theplurality of points distributed over the lens surface and the specifiedlens edge height with respect to the edge of the lens.
 21. The method ofclaim 20, wherein the rotation is controlled by an angle-dependenthanding function H(θ) such that M(ρ,θ)→M(ρ,H(θ)) and z(θ)→z(H(θ)) whereM is mean power, z(θ) is the lens edge height, and (ρ,θ) are polarcoordinates over the area of the lens.
 22. A progressive lens comprisinga surface having a variable height and including a distance area and areading area, wherein mean power over the lens surface varies accordingto a set of curves forming iso-mean power contours on the lens surfaceand a contour defining an area of constant mean power in the distancearea is an ellipse with a ratio of major axis to minor axis in the rangeof about 1.1 to 3.0.
 23. The progressive lens of claim 22, wherein meanpower M varies along a connecting path extending from a first point inthe distance area to a second point in the reading area according to afunction of the form:${M(y)} = {M_{D} + {\left\lbrack \frac{M_{R} - M_{D}}{2} \right\rbrack\left\lbrack {1 - {\cos \left( {\pi \quad \frac{y_{D} - y}{y_{D} - y_{R}}} \right)}} \right\rbrack}}$

where M_(D) is mean power specified at a first point (0,y_(D)) in thedistance area and M_(R) is mean power specified at a second point(0,y_(R)) in the reading area.
 24. The progressive lens of claim 23,where astigmatism along the connecting path is less than0.15*(M_(R)−M_(D)) where M_(D) is mean power specified at a first pointin the distance area and M_(R) is mean power specified at a second pointin the reading area.
 25. A progressive lens comprising: a distance areahaving a first mean power; a reading area having a second mean powerhigher than the first mean power; and a central area between thedistance and reading areas, the width of the central area being at leastabout 10 millimeters wide, wherein mean power increases smoothly andsubstantially monotonically throughout the central area in a directionfrom the distance area to the reading area.
 26. The progressive lens ofclaim 25, wherein the width of the central area is at least about 20millimeters wide.
 27. The progressive lens of claim 25, wherein thewidth of the central area is at least about 30 millimeters wide.
 28. Asystem for designing progressive lens comprising: a processor foraccepting inputs defining mean power variation over a coordinate systemcovering the surface of the lens and defining lens height around theedge of the lens and for calculating lens height at a plurality ofpoints over the lens surface by solving an elliptic partial differentialequation subject to the lens height at the edge of the lens as aboundary condition; and a memory for storing the calculated lens heightvalues.
 29. The system of claim 28, further comprising a numericallycontrolled milling machine for accepting the calculated lens heightvalues and using the calculated lens height values for machining thelens or a mold for producing the lens or a former for producing thelens.
 30. The system of claim 29, wherein the numerically controlledmilling machine adjusts the calculated lens height values in accordancewith the type of machining tool fitted to the milling machine.
 31. Asystem for designing progressive lens comprising: means for acceptinginputs defining mean power variation over a coordinate system coveringthe surface of the lens and defining lens height around the edge of thelens and for calculating lens height at a plurality of points over thelens surface by solving an elliptic partial differential equationsubject to the lens height at the edge of the lens as a boundarycondition; and means for storing the calculated lens height values. 32.The system of claim 31, further comprising means for accepting thecalculated lens height values and using the calculated lens heightvalues for machining the lens or a mold for producing the lens or aformer for producing the lens.
 33. A system for designing progressivelens comprising a processor for calculating lens height at a pluralityof points over the lens surface according to the method of claim 1.